Why use the output of the generator to train the discriminator in a GAN?
The main reason that the discriminator is trained concurrently with the generator is to provide (at least in theory) a smooth and gradual learning signal for the generator.

If we trained the discriminator on only the input data, then, assuming our training algorithm converges well, it should quickly converge to a fixed model. The generator can then learn to fool this fixed model, but it will likely still be easy to spot the generator's fakes for a human. For example, the discriminator may have learned that, coincidentally, in the sample you provided, all images of trucks have a fully white pixel in the top left corner. If it learns that pattern, the generator can fool it by generating noise with a white pixel. Once the generator has learned this pattern, all learning stops.

In contrast, suppose that the discriminator is repeatedly re-trained on a mixture of real and generated examples. The discriminator will be forced to learn more complex patterns than "white pixel in upper left", which improves its quality beyond the raw patterns in the sample data.

The converse relationship is also true. If the generator is trained only on the training data, it will also likely pick out only the most obvious patterns. These patterns are likely to create many local minima in the weight space for the network. However, if the error signal from the discriminator is fed to the generator, then the generator must adapt: in effect, we are telling it "making the top left pixel white is not good enough to fool observers. Find more complex patterns".